Answer
a. $\frac{a}{13}$ = $\frac{7}{b}$
b. $\frac{a-7}{7}$ = $\frac{13-b}{b}$
c. $\frac{7}{a}$ = $\frac{b}{13}$
Work Step by Step
We are given the proportion $\frac{a}{7}$ = $\frac{13}{b}$
Cross multiply
ab=7 x 13
ab = 91
Divide both sides of ab=91 by 13b
$\frac{ab}{13b}$ = $\frac{91}{13b}$
Reducing down that leaves you with $\frac{a}{13}$ = $\frac{7}{b}$
b. Start with the initial proportion of $\frac{a}{7}$ = $\frac{13}{b}$
Subtract the denominator from the numerator
$\frac{a-7}{7}$ = $\frac{13-b}{b}$
c. Reverse the original proportion
$\frac{a}{7}$ = $\frac{13}{b}$ is the same as $\frac{7}{a}$ = $\frac{b}{13}$
